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[{"key": "dc.contributor.advisor", "value": "Nurmi, Sami", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Voutilainen, Antero", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2023-02-13T08:17:54Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2023-02-13T08:17:54Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2023", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/85435", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 kandidaatin tutkielmassa johdattelen lukijan tutustumaan yleisen suhteellisuusteorian k\u00e4sitteisiin ja notaatioihin. Tutkielmassa tutustutaan muun muassa\ntensoreihin, Einsteinin yht\u00e4l\u00f6ihin sek\u00e4 aika-avaruuden kaarevuuteen ja sit\u00e4 kuvaavaan metriikkaan. Yleiseen suhteellisuusteoriaan tutustumisen lis\u00e4ksi johdan TOV\n(Tolmann-Oppenheimer-Volkoff) - yht\u00e4l\u00f6n ratkaisemalla Einstein yht\u00e4l\u00f6t yleisess\u00e4\naikainvariantissa, pallosymmetrisess\u00e4 metriikassa.\nSovellan TOV-yht\u00e4l\u00f6\u00e4 my\u00f6s valkoisten k\u00e4\u00e4pi\u00f6iden ja degeneroituneen elektronikaasun tapauksessa ja ratkaisen sen numeerisesti Python-koodilla. Ratkaisuna\nTOV-yht\u00e4l\u00f6\u00f6n saadaan valkoisen k\u00e4\u00e4pi\u00f6n rakenne, ja useaa t\u00e4hte\u00e4 mallintamalla\nsaadaan valkoisen k\u00e4\u00e4pi\u00f6n massa-s\u00e4de relaatio, josta pystyt\u00e4\u00e4n lukemaan valkoisen\nk\u00e4\u00e4pi\u00f6n maksimaalinen mahdollinen massa Chandrasekharin rajalla (noin 1.4 M\u2299,\njossa M\u2299 tarkoittaa Auringon massa). T\u00e4m\u00e4n lis\u00e4ksi vertailen relativistisen ja ep\u00e4relativistisen hydrostaattisen tasapainoyht\u00e4l\u00f6n eroa massa-s\u00e4de relaation avulla sek\u00e4\nlaskemalla eri teorioiden tiheysprofiilien v\u00e4lisen suhteen.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "In this bachelor\u2019s thesis, I introduce the reader to the concepts and notations of\ngeneral relativity. In the thesis, I will present, among other things, tensors, Einstein\u2019s\nequations and the curvature of space-time and the metric that describes it. In\naddition to familiarizing myself with the general theory of relativity, I derive the\nTOV (Tolmann-Oppenheimer-Volkoff) equation by solving the Einstein equations in\nthe general time-invariant, spherically symmetric metric.\nI apply the TOV equation also in the case of white dwarfs and degenerate\nelectron gas and solve it numerically with a Python code. As a solution to the TOV\nequation, the mass, pressure and density profile of the white dwarf is obtained. By\nmodeling several stars, the mass-radius relation of the white dwarf is obtained, from\nwhich the maximum possible mass of the white dwarf at the Chandrasekhar limit\n(approximately 1.4 M\u2299, where M\u2299 is the Solar mass) can be read. In addition to this,\nthe difference between the relativistic and non-relativistic hydrostatic equilibrium\nequations are compared using the mass-radius relation and by calculating the ratio\nbetween the density profiles of different theories.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Miia Hakanen (mihakane@jyu.fi) on 2023-02-13T08:17:54Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2023-02-13T08:17:54Z (GMT). No. of bitstreams: 0\n Previous issue date: 2023", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "64", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "TOV-yht\u00e4l\u00f6", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "valkoinen k\u00e4\u00e4pi\u00f6", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Hydrostaattinen tasapainoyht\u00e4l\u00f6 yleisess\u00e4 suhteellisuusteoriassa valkoisen k\u00e4\u00e4pi\u00f6n sovelluksessa", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "bachelor thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202302131725", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Bachelor's thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Kandidaatinty\u00f6", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Fysiikan laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Physics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Fysiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Physics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_7a1f", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "bachelorThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4021", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "astrofysiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "suhteellisuusteoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "fysiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "yht\u00e4l\u00f6t", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "kosmologia", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "maailmankaikkeus", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "avaruus", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "formalismi", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "k\u00e4\u00e4pi\u00f6t\u00e4hdet", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
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